Prior art position sensors are known which make use of a variable transformer. In simple transformer parlance an M turn primary coil with current "I" passing through the M turns induces a flux in the transformer secondary given by: EQU F1 = M*I/R (1)
where F1 is the magnetic flux (flux) and R is the reluctance of the magnetic path linking the primary to the secondary. When the magnetic permeability of a yoke linking the primary to the transformer secondary is sufficiently low virtually all of the flux induced by the primary will be confined in the yoke and result in the flux being approximately constant throughout the transformer (i.e. magnetic circuit of the transformer). This allows most of the flux produced in the primary (some leakage of flux from the yoke is inevitable) to also link the secondary. Often a small air gap is used to provide the bulk of the reluctance in the reluctance path (magnetic circuit) and thereby minimize effects due to variations of permeability in the yoke due to material or temperature changes. The flux "F1" induced by the primary will then induce an emf in the secondary given by: EQU V.sub.sec = -f*(dF1/dt)*N EQU = -f*M*N/R*(dI/dt) (2)
where "f" is a factor representing the fraction of the flux "F1" produced in the primary that passes through the secondary and "N" is the number of turns of the secondary. The factor "f" is generally dependent on the geometry and permeabilities of the various elements in the reluctance paths linking the primary and secondary coils. In an ideal transformer f=1. Not mentioned but relevant are hysteresis effects that can effect f & R and core and wire losses that can effect the overall power efficiency of the transformers. Variations in geometry and materials to minimize hysteresis effects, inefficiencies, size, and weight are the basis for a broad range of transformer applications.
The key factors to note in the "fixed" transformer design are:
(a) The designs are optimized to minimize the flux loss "f" between the primary and secondary.
(b) In normal operation the reluctance of the flux paths (magnetic circuit) associated with the transformer remain constant.
(c) The number of turns on the primary "M" and secondary "N" remain constant.